The relationship between the stasheff polytope and painted trees using Tubings

الملخص EN

A polytope plays a central role in different areas of mathematics.

It is used quite heavily in applied fields of mathematics, such as medical imaging and robotics, geometric modeling.

A polytope has many users in modern science such as computer graphics, optimization, and search engine.

It is intended for a broad audience of mathematically inclined.

Therefore in this paper, we shall take a polytope with one kind of application, which is known as a Stasheff polytope.

it has been applied in: moduli spaces, Erhart polynomial, physics- chemistry, and Hopf algebras.

In this paper, a finite graph G with tubing is taken, the nodes of the graph are reduce to points in R? and the convex hull for them are simplex, permutahedron and associahedron (Stasheff polytope ) are studied.

Also, a fan graph to the painted tree is also taken and reduces its nodes to points in ??.

The converse of this result is also given with different examples to consult our results